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Results (3 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
27864.3-a1 27864.3-a \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{4} \cdot 43 \) $0$ $\mathsf{trivial}$ $1$ $0.665946086$ 0.941789987 \( \frac{21226369178}{19320201} a - \frac{50204656630}{19320201} \) \( \bigl[a\) , \( a\) , \( a\) , \( -82 a - 21\) , \( 357 a - 286\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-82a-21\right){x}+357a-286$
27864.3-b1 27864.3-b \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{4} \cdot 43 \) $0$ $\mathsf{trivial}$ $1$ $0.475602017$ 2.017808469 \( \frac{4221782747113658}{7339102499889} a + \frac{29753937148295630}{7339102499889} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 68 a - 238\) , \( 512 a - 1058\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(68a-238\right){x}+512a-1058$
27864.3-c1 27864.3-c \(\Q(\sqrt{-2}) \) \( 2^{3} \cdot 3^{4} \cdot 43 \) $1$ $\mathsf{trivial}$ $0.118626377$ $1.873745711$ 5.658214722 \( -\frac{187524338}{846369} a + \frac{1460733730}{846369} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 3 a + 13\) , \( 2 a + 6\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a+13\right){x}+2a+6$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.